MATH 462 - DIFFERENTIAL GEOMETRY

This is an introductory course on differential geometry of curves and surfaces; the only

prerequisite is multivariable calculus (Math 241 or 247 at U.T.K.). The intended audience includes

students (undergaduate or graduate) interested in applications of surface geometry

(to areas such as image processing, computer graphics, optimal design, engineering, architecture, materials sciences and physics.)

Main topics:

- Curves in the plane and in space: curvature, torsion, Frenet formulas
- Surfaces: first and second fundamental forms, Gauss curvature, mean curvature
- Gauss- Weingarten and Codazzi equations
- The fundamental theorem of surface theory
- Geodesics and geodesic coordinates on surfaces
- Non-euclidean geometry
- The Gauss- Bonnet theorem
- Conformal and isometric mappings
- Introduction to minimal surfaces

minimal surface gallery (M. Weber)

References:

M.P. do Carmo, Differential Geometry of Curves and Surfaces

B. O'Neill, Elementary Differential Geometry

D.J. Struik, Lectures on Classical Differential Geometry, Dover paperback (most likely text for the course)

Grading: based on weekly problem sets and (if necessary) a written final.